The model:
One specific voter has sincere ratings
in [0,1] for each of C candidates.
(The sincere ratings were randomly and independently
determined uniform random reals in [0,1].)
There are V other voters, each of whom submits an independent random-uniform score in [0,1]
as her vote for each candidate.
These voting strategies are tested:

Sincere.
This voter rates the candidates sincerely even if this means
she doesn't use the top or bottom ratings.

Plurality. Voter awards the maximum
range vote to the best candidate (in her view) and min to all others.

Scaled sincerity.
Voter linearly transforms utilities to make best have rescaled utility 1, worst 0,
and rest linearly interpolated, then uses that as her vote.

"Acceptables" strategy. The voter gives max to every candidate worth
0.5 or more, and min to the others. (This can mean that the voter gives a
1 to every candidate, or a 0 to every candidate.)

Mean-based thresholding. The voter gives max to every candidate
at least as good as the average value of all candidates, and gives min
to the others.

Bisector-based thresholding. The voter gives max to every candidate
at least as good as the average value of the two extreme candidates, and gives min
to the others.

Maxing+sincerity: All scores sincere except the best candidate gets 1 and the worst 0.

Top-two: Give max score to the best two candidates, min to everybody else.

Bisect penultimates:
The voter gives max to every candidate
at least as good as the average value of the two "penultimate" (2nd best and 2nd worst)
candidates, and gives min to the others.

Top-three: Give max score to the top three candidates, min to everybody else.

And the winning strategies (shown blue) are...
scaled sincerity, plurality, top-two, top-three,
bisector-based thresholding, and mean-based-thresholding
(depending on the number of candidates and voters)!

C=3 candidates; 1,300,000 trials; expected utilities for the one voter, shown
(causes standard errors to be about 3 units in the last decimal place).
Scaled-sincerity (strategy C, shown pink) is not bad: it always gets ≥91% of
the best strategy's utility (among strategies A-J tried) no matter what
number of other voters V=0-100 there are, and there is
no other strategy (among A-J) that can say that! So honesty can pay!

V

A

B

C

D

E

F

G

H

I

J

0

0.2504

0.2504

0.2504

0.1877

0.2191

0.2191

0.2504

0.1253

0.1253

0.0000

1

0.1753

0.2503

0.2294

0.1876

0.2189

0.2189

0.2252

0.1250

0.1250

0.0000

2

0.1424

0.2221

0.2029

0.1719

0.2006

0.2006

0.1976

0.1219

0.1219

0.0000

3

0.1229

0.1982

0.1827

0.1574

0.1836

0.1836

0.1772

0.1164

0.1164

0.0000

4

0.1097

0.1799

0.1672

0.1453

0.1696

0.1696

0.1618

0.1109

0.1109

0.0000

5

0.1000

0.1651

0.1547

0.1354

0.1580

0.1580

0.1495

0.1057

0.1057

0.0000

6

0.0926

0.1534

0.1449

0.1275

0.1486

0.1486

0.1399

0.1016

0.1016

0.0000

7

0.0867

0.1435

0.1365

0.1203

0.1404

0.1404

0.1316

0.0972

0.0972

0.0000

8

0.0816

0.1351

0.1294

0.1143

0.1334

0.1334

0.1248

0.0937

0.0937

0.0000

9

0.0779

0.1285

0.1237

0.1093

0.1278

0.1278

0.1193

0.0905

0.0905

0.0000

10

0.0739

0.1223

0.1184

0.1049

0.1223

0.1223

0.1140

0.0876

0.0876

0.0000

11

0.0705

0.1166

0.1134

0.1006

0.1175

0.1175

0.1091

0.0848

0.0848

0.0000

12

0.0680

0.1122

0.1095

0.0973

0.1135

0.1135

0.1053

0.0824

0.0824

0.0000

13

0.0652

0.1075

0.1053

0.0937

0.1093

0.1093

0.1013

0.0798

0.0798

0.0000

14

0.0628

0.1037

0.1018

0.0907

0.1058

0.1058

0.0979

0.0778

0.0778

0.0000

15

0.0612

0.1004

0.0990

0.0881

0.1028

0.1028

0.0952

0.0760

0.0760

0.0000

20

0.0534

0.0872

0.0871

0.0777

0.0907

0.0907

0.0838

0.0683

0.0683

0.0000

25

0.0481

0.0780

0.0787

0.0703

0.0820

0.0820

0.0757

0.0628

0.0628

0.0000

30

0.0439

0.0711

0.0722

0.0646

0.0753

0.0753

0.0694

0.0580

0.0580

0.0000

40

0.0381

0.0612

0.0628

0.0562

0.0656

0.0656

0.0603

0.0513

0.0513

0.0000

50

0.0342

0.0546

0.0564

0.0505

0.0590

0.0590

0.0541

0.0467

0.0467

0.0000

60

0.0312

0.0497

0.0517

0.0464

0.0542

0.0542

0.0496

0.0431

0.0431

0.0000

70

0.0290

0.0460

0.0480

0.0430

0.0502

0.0502

0.0461

0.0402

0.0402

0.0000

80

0.0273

0.0430

0.0451

0.0404

0.0472

0.0472

0.0433

0.0379

0.0379

0.0000

90

0.0256

0.0404

0.0425

0.0381

0.0445

0.0445

0.0408

0.0359

0.0359

0.0000

100

0.0245

0.0386

0.0407

0.0366

0.0427

0.0427

0.0391

0.0346

0.0346

0.0000

100

0.024286

0.038302

0.040446

0.036370

0.042393

0.042393

0.038818

0.034330

0.034330

0.000000

1000

0.007703

0.011686

0.012809

0.011514

0.013447

0.013447

0.012266

0.011343

0.011343

0.000000

10000

0.002429

0.003667

0.004041

0.003641

0.004258

0.004258

0.003879

0.003633

0.003633

0.000000

100000

0.000779

0.001159

0.001284

0.001151

0.001344

0.001344

0.001237

0.001155

0.001155

0.000000

1000000

0.000248

0.000362

0.000411

0.000369

0.000430

0.000430

0.000395

0.000371

0.000371

0.000000

C=5 candidates;
2,500,000 trials
(causes standard errors to be about 2 units in the last decimal place).
Scaled-sincerity (strategy C, shown pink) is not bad: it always gets ≥80% of
the best strategy's utility (among strategies A-J tried) no matter what
number of other voters V=0-1000 there are, and there is
no other strategy (among A-J) that can say that! So honesty can pay!

V

A

B

C

D

E

F

G

H

I

J

0

0.3329

0.3329

0.3329

0.2340

0.2332

0.2444

0.3329

0.2497

0.2219

0.1664

1

0.2387

0.3334

0.2788

0.2345

0.2336

0.2449

0.2749

0.2499

0.2222

0.1668

2

0.1944

0.2813

0.2428

0.2203

0.2249

0.2315

0.2337

0.2407

0.2163

0.1650

3

0.1685

0.2430

0.2167

0.2051

0.2122

0.2161

0.2061

0.2252

0.2051

0.1594

4

0.1506

0.2149

0.1971

0.1914

0.1996

0.2021

0.1862

0.2102

0.1936

0.1528

5

0.1371

0.1928

0.1816

0.1792

0.1880

0.1896

0.1708

0.1967

0.1829

0.1463

6

0.1273

0.1765

0.1698

0.1696

0.1788

0.1797

0.1592

0.1859

0.1742

0.1408

7

0.1187

0.1630

0.1595

0.1606

0.1699

0.1702

0.1490

0.1757

0.1657

0.1350

8

0.1123

0.1520

0.1515

0.1538

0.1631

0.1632

0.1413

0.1678

0.1592

0.1306

9

0.1061

0.1424

0.1438

0.1467

0.1560

0.1557

0.1340

0.1598

0.1524

0.1259

10

0.1014

0.1347

0.1377

0.1411

0.1501

0.1498

0.1281

0.1533

0.1468

0.1221

11

0.0970

0.1278

0.1322

0.1359

0.1449

0.1444

0.1229

0.1474

0.1417

0.1184

12

0.0933

0.1219

0.1272

0.1313

0.1400

0.1394

0.1181

0.1420

0.1371

0.1149

13

0.0898

0.1164

0.1228

0.1271

0.1358

0.1351

0.1139

0.1373

0.1329

0.1119

14

0.0868

0.1117

0.1189

0.1233

0.1317

0.1310

0.1102

0.1329

0.1290

0.1090

15

0.0838

0.1076

0.1150

0.1196

0.1279

0.1271

0.1066

0.1288

0.1254

0.1061

16

0.0815

0.1037

0.1119

0.1164

0.1247

0.1237

0.1037

0.1253

0.1223

0.1039

17

0.0790

0.1001

0.1086

0.1132

0.1213

0.1204

0.1005

0.1216

0.1189

0.1014

18

0.0770

0.0969

0.1058

0.1105

0.1186

0.1176

0.0980

0.1187

0.1163

0.0994

19

0.0751

0.0941

0.1035

0.1082

0.1161

0.1151

0.0957

0.1159

0.1139

0.0976

20

0.0735

0.0917

0.1012

0.1058

0.1137

0.1127

0.0936

0.1134

0.1115

0.0958

25

0.0658

0.0807

0.0910

0.0959

0.1030

0.1020

0.0840

0.1021

0.1011

0.0874

30

0.0604

0.0730

0.0836

0.0882

0.0948

0.0938

0.0771

0.0935

0.0931

0.0813

35

0.0557

0.0664

0.0773

0.0817

0.0882

0.0871

0.0713

0.0865

0.0866

0.0759

40

0.0525

0.0620

0.0729

0.0771

0.0832

0.0822

0.0672

0.0813

0.0818

0.0720

45

0.0495

0.0580

0.0688

0.0729

0.0787

0.0777

0.0633

0.0767

0.0774

0.0683

50

0.0469

0.0546

0.0652

0.0693

0.0748

0.0738

0.0601

0.0727

0.0735

0.0651

60

0.0430

0.0492

0.0598

0.0635

0.0686

0.0677

0.0550

0.0664

0.0675

0.0601

70

0.0399

0.0454

0.0556

0.0591

0.0638

0.0630

0.0512

0.0616

0.0628

0.0561

80

0.0373

0.0421

0.0520

0.0553

0.0597

0.0589

0.0478

0.0575

0.0588

0.0527

90

0.0352

0.0395

0.0490

0.0522

0.0565

0.0557

0.0451

0.0543

0.0556

0.0500

100

0.0335

0.0373

0.0467

0.0499

0.0539

0.0532

0.0430

0.0516

0.0530

0.0477

200

0.0237

0.0257

0.0332

0.0354

0.0383

0.0377

0.0305

0.0364

0.0377

0.0344

300

0.0194

0.0208

0.0271

0.0290

0.0314

0.0309

0.0249

0.0296

0.0309

0.0283

400

0.0168

0.0177

0.0234

0.0250

0.0271

0.0267

0.0215

0.0255

0.0267

0.0245

500

0.0149

0.0158

0.0210

0.0224

0.0243

0.0239

0.0192

0.0228

0.0239

0.0220

600

0.0137

0.0144

0.0192

0.0205

0.0223

0.0219

0.0176

0.0209

0.0219

0.0202

700

0.0127

0.0133

0.0178

0.0191

0.0207

0.0204

0.0164

0.0194

0.0203

0.0187

800

0.0118

0.0124

0.0166

0.0177

0.0192

0.0190

0.0152

0.0180

0.0189

0.0175

900

0.0112

0.0117

0.0156

0.0167

0.0181

0.0179

0.0144

0.0170

0.0179

0.0165

1000

0.0106

0.0111

0.0149

0.0159

0.0173

0.0170

0.0137

0.0161

0.0170

0.0157

1000

0.010610

0.011064

0.014841

0.015913

0.017225

0.016960

0.013634

0.016122

0.016952

0.015677

10000

0.003360

0.003377

0.004678

0.005026

0.005443

0.005363

0.004309

0.005041

0.005369

0.005031

100000

0.001037

0.001049

0.001459

0.001571

0.001707

0.001681

0.001338

0.001570

0.001675

0.001573

1000000

0.000340

0.000345

0.000479

0.000513

0.000556

0.000543

0.000439

0.000511

0.000547

0.000516

C=9 candidates;
1,300,000 trials each
(causes standard errors to be about 3 units in the last decimal place).
Scaled-sincerity (strategy C, shown pink) is not bad: it always gets ≥78% of
the best strategy's utility (among strategies A-J tried) no matter what
number of other voters V=0-1000000 there are, and there is
no other strategy (among A-J) that can say that! So honesty can pay!

V

A

B

C

D

E

F

G

H

I

J

0

0.4005

0.4005

0.4005

0.2494

0.2412

0.2503

0.4005

0.3504

0.2461

0.3004

1

0.2995

0.4002

0.3200

0.2491

0.2408

0.2499

0.3185

0.3500

0.2455

0.3000

2

0.2455

0.3150

0.2755

0.2440

0.2389

0.2456

0.2659

0.3299

0.2429

0.2945

3

0.2135

0.2605

0.2451

0.2346

0.2325

0.2371

0.2327

0.2989

0.2353

0.2793

4

0.1913

0.2226

0.2227

0.2235

0.2231

0.2262

0.2095

0.2712

0.2252

0.2620

5

0.1746

0.1957

0.2048

0.2126

0.2135

0.2155

0.1918

0.2481

0.2149

0.2458

6

0.1615

0.1746

0.1907

0.2026

0.2044

0.2057

0.1775

0.2286

0.2055

0.2316

7

0.1510

0.1587

0.1790

0.1936

0.1961

0.1966

0.1662

0.2128

0.1967

0.2189

8

0.1423

0.1458

0.1694

0.1856

0.1887

0.1888

0.1569

0.1994

0.1892

0.2080

9

0.1356

0.1354

0.1615

0.1789

0.1822

0.1819

0.1494

0.1884

0.1825

0.1990

10

0.1289

0.1265

0.1543

0.1728

0.1761

0.1758

0.1422

0.1785

0.1763

0.1904

11

0.1238

0.1193

0.1483

0.1671

0.1707

0.1701

0.1366

0.1701

0.1708

0.1829

12

0.1185

0.1125

0.1422

0.1614

0.1651

0.1644

0.1309

0.1619

0.1651

0.1757

13

0.1142

0.1070

0.1373

0.1566

0.1605

0.1595

0.1262

0.1553

0.1605

0.1697

14

0.1104

0.1019

0.1328

0.1521

0.1560

0.1550

0.1219

0.1493

0.1559

0.1640

15

0.1072

0.0976

0.1291

0.1487

0.1527

0.1515

0.1185

0.1440

0.1524

0.1593

16

0.1041

0.0940

0.1252

0.1447

0.1484

0.1473

0.1151

0.1393

0.1481

0.1544

17

0.1010

0.0903

0.1218

0.1413

0.1452

0.1440

0.1117

0.1347

0.1449

0.1502

18

0.0979

0.0869

0.1184

0.1379

0.1418

0.1405

0.1084

0.1304

0.1415

0.1459

19

0.0957

0.0840

0.1155

0.1349

0.1388

0.1375

0.1058

0.1267

0.1385

0.1424

20

0.0932

0.0812

0.1126

0.1318

0.1356

0.1343

0.1030

0.1229

0.1352

0.1386

25

0.0840

0.0708

0.1018

0.1202

0.1240

0.1226

0.0930

0.1090

0.1235

0.1247

30

0.0767

0.0627

0.0931

0.1107

0.1143

0.1128

0.0850

0.0981

0.1138

0.1135

35

0.0711

0.0570

0.0864

0.1030

0.1067

0.1052

0.0788

0.0899

0.1061

0.1049

40

0.0668

0.0527

0.0813

0.0972

0.1006

0.0992

0.0740

0.0836

0.1001

0.0983

45

0.0634

0.0492

0.0770

0.0924

0.0957

0.0944

0.0702

0.0785

0.0952

0.0926

50

0.0601

0.0460

0.0731

0.0878

0.0910

0.0897

0.0666

0.0739

0.0904

0.0877

60

0.0548

0.0413

0.0668

0.0806

0.0837

0.0824

0.0608

0.0669

0.0831

0.0799

70

0.0507

0.0376

0.0619

0.0748

0.0777

0.0765

0.0563

0.0612

0.0772

0.0735

80

0.0476

0.0350

0.0582

0.0704

0.0731

0.0719

0.0528

0.0572

0.0726

0.0688

90

0.0451

0.0323

0.0548

0.0665

0.0691

0.0679

0.0499

0.0533

0.0687

0.0647

100

0.0427

0.0308

0.0522

0.0635

0.0660

0.0649

0.0474

0.0508

0.0655

0.0617

100

0.042540

0.030310

0.051871

0.063042

0.065528

0.064403

0.047147

0.050224

0.065099

0.061136

1000

0.013558

0.008594

0.016571

0.020297

0.021141

0.020733

0.015017

0.014783

0.020983

0.018698

10000

0.004330

0.002620

0.005287

0.006448

0.006708

0.006600

0.004805

0.004576

0.006654

0.005871

100000

0.001357

0.000824

0.001671

0.002041

0.002125

0.002092

0.001510

0.001444

0.002107

0.001848

1000000

0.000465

0.000276

0.000572

0.000689

0.000714

0.000704

0.000520

0.000487

0.000711

0.000628

Conclusions

Strategy E (mean-based thresholding) is the best strategy here
when the number V of other voters is sufficiently large, while strategy
B (plurality-style) is the best when V>0 is sufficiently small.
Furthermore, I believe E obtains
the asymptotically maximum possible
expected utility for any zero-info voting strategy
when V→∞.

The "honest" scaled-sincerity strategy C does impressively well.
I can prove (below) that it always does at least 2/3 as well as strategy E
(no matter what the number of candidates is) when V→∞,
and I conjecture it always does at least 2/3 as well as any strategy.

Furthermore, in any election situation at all
C always is better than (or at least as good as)
not voting at all. This obvious claim may not sound
enormously impressive, but note that instant runoff voting IRV, as well as all Condorcet voting
systems, fail that criterion.

Some Theorems and Proofs

Theorem:
Mean-based thresholding is optimal range-voting strategy in the limit of
a large number of other voters, each random independent full-range.

Proof:
In this limit, it should be clear that
the optimal strategy is to choose the threshold to maximize the
sum of across-threshold utility-pair-differences.
This sum has A·B
terms if there are A below-threshold and B above-threshold candidates,
and it is proportional in our model & limit to the expected increase in your utility that you
get by voting using that threshold (versus if you had not voted).

What is not obvious, and what we shall now prove, is that this is the
same thing as mean-based thresholding.

Let there be A utilities below threshold and B above.
Let their means be μA and μB respectively,
and the mean of the entire utility-set is μ
where (A+B)μ = AμA+BμB.
Consider moving the threshold slightly so
that the greatest below-threshold utility X becomes above-threshold.
The amount by which the
sum of across-threshold utility-pair-differences
changes (additively) is

Δ =
(A-1) (B+1) [ (BμB+X)/(B+1) -
(AμA-X)/(A-1) ]
-
A B (μB-μA)

which after simplification is the same as

Δ = (A+B)(X-μ).

Notice that Δ is positive (i.e. the movement of the threshold
was good, according to
the expected utility difference)
if and only if μ<X (i.e. if and only if it was good according to
the mean-based-thresholding criterion).

The best situation is when no motion can improve utility, and that happens
when the threshold is exactly located at μ.
Q.E.D.

Theorem:
The "honest" scaled-sincerity strategy C
always does at least 2/3 as well as the mean-based thresholding strategy E
(no matter what the number of candidates is) in the V→∞ limit.

Proof sketch:
The expected utility of scaled-sincerity is lower-bounded by the first sum
below (in an n-candidate election),
while the expected utility of mean-based thresholding is upper-bounded by
the second sum below (up to some common V-dependent proportionality factor) in the
V→∞ limit:

The ratio of the closed-form summations given, plainly is 2/3 or greater.
Q.E.D.

Remark:
The 2/3 ratio actually is attained
in the double limit when V→∞ and the number
of candidates also goes to infinity. That is because

∫∫0≤x<y≤1 (y-x)2 dxdy = 1/12
and
∫∫0≤x≤½≤y≤1 (y-x) dxdy = 1/8.

Conjecture:Scaled-sincerity strategy C
always does at least 2/3 as well as the optimum possible voting strategy,
no matter what the number of candidates and voters are.

That was based on the above theoretical indications, my experiments here, and also
other experiments by Kevin Venzke.

Open question 1:
Settle this conjecture.

Open question 2:
since the best strategy (among A-J) changes when you
change the numbers V of voters and C of candidates – can you cook up a simple universal
strategy that knows C and V, and which always outperforms or equals all of the
strategies above?